This application claims the priority of Japanese Patent Application No. 2000-037777 filed on Feb. 16, 2000, which is incorporated herein by reference.
1. Field of the Invention
The present invention relates to a fringe analysis method using Fourier transform; and, in particular, to a fringe analysis method which can effectively use Fourier transform technique when analyzing image data having fringe patterns such as interference fringe patterns.
2. Description of the Prior Art
Light-wave interferometry has conventionally been known as important means concerning accurate measurement of wavefront. In recent years, there has been urgent need for developing an interferometry technique (sub-fringe interferometry) for reading out information from a fraction of a single interference fringe (one fringe) or less from the necessity to measure a surface or wavefront aberration of at an accuracy of {fraction (1/10)} wavelength or higher.
For sub-fringe interferometry techniques, attention has been focused on techniques using Fourier transform method as disclosed in xe2x80x9cBasics of Sub-fringe Interferometry,xe2x80x9d Kogaku, Vol. 13, No. 1 (February, 1984), pp. 55-65, for example.
However, Fourier transform method, which is excellent in principle, leaves some problems unsolved and has not always been effectively put into practice.
One of such problems lies in that a large error may occur in Fourier transform of an effective data area in fringe image data if the effective data area has a form different from that of the area subjected to Fourier transform method.
While the area subjected to Fourier transform method is typically the whole area of image data (having a rectangular form in general) obtained by imaging, results of Fourier transform method in the effective data area may include a large error if the form of effective data area is only a part (having a circular form, for example) of the whole area.
Therefore, in such a case, so-called masking processing may be applied to, in which the effective data area and the other area are multiplied by coefficients of 1 and 0, respectively, before carrying out Fourier transform method.
When fringe image data is subjected to such masking processing, a large gap (edge or discontinuity) may occur at the boundary between the effective and ineffective data areas. Since Fourier transform method does not always function effectively for data having such a gap (edge or discontinuity), its results of data analysis in the vicinity of the boundary may include an error larger than that yielded without the masking processing.
In particular, since the effective data area may vary greatly depending on the forms of wavefront and regions to be observed, a technique which minimizes the error is demanded. Techniques involving the above-mentioned masking processing have not been satisfactory yet from such a viewpoint as well.
In view of the circumstances mentioned above, it is an object of the present invention to provide a fringe analysis technique which can yield, in response to the wavefront of an effective data area in fringe image data, favorable analysis results of the effective data area with less errors after Fourier transform method.
The present invention provides a fringe analysis method using Fourier transform, the method comprising the step of subjecting fringe image data carrying wavefront information to be observed to Fourier transform method so as to determine the wavefront;
wherein, before the Fourier transform method is applied to, the fringe image data is multiplied by a window function corresponding to an effective data area of the fringe image data.
The wavefront information may be surface profile information of the object.
When the fringe image data is two-dimensional image data having a rectangular form, it is preferred that the window function be a function represented by variables indicating respective positions in two directions orthogonal to each other.
When the fringe image data is two-dimensional image data having a circular form, it is preferred that the window function be a function represented by a variable indicating a radial position from a center which is located at substantially the center position of the circular form.
The window function may have a form corresponding to that of the effective data area.
When the effective data area of the fringe image data has a form surrounding an effective data area in this case, it is preferred that the window function be a partial window function having a form corresponding to that of the effective data area.
As the partial window function, a ring type window function having a ring shape is used, for example.
The fringe image data may be interference fringe image data.